Abstract
The paper deals with the theoretical analysis of a regularized logarithmic barrier method for solving ill-posed convex programming problems. In this method a multi-step proximal regularization of the auxiliary problems is performed in the framework of the interior point approach. The termination of the proximal terations for each auxiliary problem is controlled by means of estimates, characterizing the efficiency of the iterations. A special deleting rule permits to use only a part of the constraints of the original problem for constructing the auxiliary Problems. Convergence and rate of convergence of the method suggested are studied as well as its stability with respect to data perturbations. An example is given showing the behavior of the classical barrier method in the case of ill-posed convex programming problems.
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